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Prof. Dr. Achim Ilchmann

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Ilchmann, Achim; Pham Huu Anh, Ngoc
Stability and robust stability of positive Volterra systems. - In: International journal of robust and nonlinear control : IFAC affiliated journal.. - New York, NY [u.a.] : Wiley, ISSN 1099-1239, Bd. 22 (2012), 6, S. 604-629
Berger, Thomas; Reis, Timo
Controllability of linear differential-algebraic systems - a survey. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2012. - Online-Ressource (PDF-Datei: 48 S., 501 KB). . - (Preprint. - M12,03)

Different concepts related to controllability of differential-algebraic equations are described. The class of systems considered consists of linear differential-algebraic equations with constant coefficients. Regularity, which is, loosely speaking, a concept related to existence and uniqueness of solutions for any inhomogeneity, is not required in this article. The concepts of impulse controllability, controllability at infinity, behavioral controllability, strong and complete controllability are described and defined in time-domain. Equivalent criteria that generalize the Hautus test are presented and proved. - Special emphasis is placed on normal forms under state space transformation and, further, under state space, input and feedback transformations. Special forms generalizing the Kalman decomposition and Brunovsky form are presented. Consequences for state feedback design and geometric interpretation of the space of reachable states in terms of invariant subspaces are proved.
Azizov, Tomas Ya.; Trunk, Carsten
PT symmetric, Hermitian and P-self-adjoint operators related to potentials in PT quantum mechanics. - In: Journal of mathematical physics. - College Park, Md. : American Inst. of Physics, ISSN 1089-7658, Bd. 53 (2012), 1, S. 012109, insges. 18 S.
Arendt, Wolfgang; Ball, Joseph A.; Behrndt, Jussi; Förster, Karl-Heinz; Mehrmann, Volker; Trunk, Carsten
Spectral theory, mathematical system theory, evolution equations, differential and difference equations : 21st International Workshop on Operator Theory and Applications, Berlin, July 2010. - Basel : Birkhäuser, 2012. - VIII, 690 S.. . - (Operator theory: advances and applications. - Vol. 221) ISBN 3-0348-0296-X
- Literaturangaben

Homburg, Ale Jan; Jukes, Alice C.; Knobloch, Jürgen; Lamb, Jeroen S. W.;
Bifurcation from codimension one relative homoclinic cycles. - In: Transactions of the American Mathematical Society. - Providence, RI : Soc., ISSN 1088-6850, Bd. 363 (2011), 11, S. 5663-5701
Ilchmann, Achim; Ke, Zhenqing; Logemann, Hartmut
Indirect sampled-data control with sampling period adaptation. - In: International journal of control. - London : Taylor & Francis, ISSN 1366-5820, Bd. 84 (2011), 2, S. 424-431
Knobloch, Jürgen; Lloyd, David J. B.; Sandstede, Björn; Wagenknecht, Thomas
Isolas of 2-pulse solutions in homoclinic snaking scenarios. - In: Journal of dynamics and differential equations. - New York, NY [u.a.] : Springer Science + Business Media B.V., ISSN 1572-9222, Bd. 23 (2011), 1, S. 93-114
Hill, Adrian T.; Ilchmann, Achim
Exponential stability of time-varying linear systems. - In: IMA journal of numerical analysis : IMAJNA.. - Oxford : Oxford Univ. Press, ISSN 1464-3642, Bd. 31 (2011), 3, S. 865-885
Philipp, Friedrich; Ran, André C. M.; Wojtylak, Michał
Local definitizability of T [*]T and TT[*]. - In: Integral equations and operator theory : IEOT.. - Berlin : Springer, ISSN 1420-8989, Bd. 71 (2011), 4, S. 491-508
Behrndt, Jussi; Möws, Roland; Trunk, Carsten
Eigenvalue estimates for singular left-definite Sturm-Liouville operators. - In: Journal of spectral theory. - Zürich : EMS Publishing House, ISSN 1664-0403, Bd. 1 (2011), 3, S. 327-347

The spectral properties of a singular left-definite Sturm-Liouville operator $JA$ are investigated and described via the properties of the corresponding right-definite selfadjoint counterpart $A$ which is obtained by substituting the indefinite weight function by its absolute value. The spectrum of the $J$-selfadjoint operator $JA$ is real and it follows that an interval $(a,b)\subset\dR^+$ is a gap in the essential spectrum of $A$ if and only if both intervals $(-b,-a)$ and $(a,b)$ are gaps in the essential spectrum of the $J$-selfadjoint operator $JA$. As one of the main results it is shown that the number of eigenvalues of $JA$ in $(-b,-a) \cup (a,b)$ differs at most by three of the number of eigenvalues of $A$ in the gap $(a,b)$; as a byproduct results on the accumulation of eigenvalues of singular left-definite Sturm-Liouville operators are obtained. Furthermore, left-definite problems with symmetric and periodic coefficients are treated, and several examples are included to illustrate the general results.